Related papers: Fitting a function to time-dependent ensemble aver…
In this paper, we present a progressive and iterative approximation method with memory for least square fitting(MLSPIA). It adjusts the control points and the weighted sums iteratively to construct a series of fitting curves (surfaces) with…
Constructing prediction intervals for time series forecasting is challenging, particularly when practitioners rely solely on point forecasts. While previous research has focused on creating increasingly efficient intervals, we argue that…
We study the functional linear regression model with a scalar response and a Hilbert space-valued predictor, a canonical example of an ill-posed inverse problem. We show that the functional partial least squares (PLS) estimator attains…
Electrochemical impedance spectroscopy (EIS) data is typically modeled using an equivalent circuit model (ECM), with parameters obtained by minimizing a loss function via nonlinear least squares fitting. This paper introduces two new loss…
Ensemble data assimilation techniques form an indispensable part of numerical weather prediction. As the ensemble size grows and model resolution increases, the amount of required storage becomes a major issue. Data compression schemes may…
Functional principal component analysis has been shown to be invaluable for revealing variation modes of longitudinal outcomes, which serves as important building blocks for forecasting and model building. Decades of research have advanced…
We report a possible solution to the trouble that the covariance fitting fails when the data is highly correlated and the covariance matrix has small eigenvalues. As an example, we choose the data analysis of highly correlated $B_K$ data on…
We propose a multilevel Monte-Carlo scheme, applicable to local actions, which is expected to reduce statistical errors on correlation functions. We give general arguments to show how the efficiency and parameters of the algorithm are…
We propose a flexible dual functional factor model for modelling high-dimensional functional time series. In this model, a high-dimensional fully functional factor parametrisation is imposed on the observed functional processes, whereas a…
We present a Bayesian approach for modeling multivariate, dependent functional data. To account for the three dominant structural features in the data--functional, time dependent, and multivariate components--we extend hierarchical dynamic…
In this notes we describe an algorithm for non-linear fitting which incorporates some of the features of linear least squares into a general minimum $\chi^2$ fit and provide a pure Python implementation of the algorithm. It consists of the…
Given a data set (t_i, y_i), i=1,..., n with the t_i in [0,1] non-parametric regression is concerned with the problem of specifying a suitable function f_n:[0,1] -> R such that the data can be reasonably approximated by the points (t_i,…
Many mathematical modelling tasks (such as in Economics and Finance) are informed by data that is "found" rather than being the result of carefully designed experiments. This often results in data series that are short, noisy,…
The construction of valid and flexible cross-covariance functions is a fundamental task for modeling multivariate space-time data arising from climatological and oceanographical phenomena. Indeed, a suitable specification of the covariance…
We study the problem of detecting and localizing multiple changes in the mean parameter of a Banach space-valued time series. The goal is to construct a collection of narrow confidence intervals, each containing at least one (or exactly…
We study additive function-on-function regression where the mean response at a particular time point depends on the time point itself as well as the entire covariate trajectory. We develop a computationally efficient estimation methodology…
We propose a spatio-temporal data-fusion framework for point data and gridded data with variables observed on different spatial supports. A latent Gaussian field with a Mat\'ern-SPDE prior provides a continuous space representation, while…
Two new methods are proposed for linear regression analysis for data with measurement errors. Both methods are designed to accommodate intrinsic scatter in addition to measurement errors. The first (BCES) is a direct extension of the…
Classical optimization theory deals with fixed, time-invariant objective functions. However, time-varying optimization has emerged as an important subject for decision-making in dynamic environments. In this work, we study the problem of…
The Zarantonello fixed-point iteration is an established linearization scheme for quasilinear PDEs with strongly monotone and Lipschitz continuous nonlinearity in Hilbert spaces. This paper presents a weighted least-squares minimization for…